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<p>We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_440_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that does not induce a homomorphism even between (untwisted) Toeplitz algebras. We prove that the twisted <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_440_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras of a jointly faithful self-similar action of a countable discrete amenable groupoid on a row-finite <i>k</i>-graph with no sources, with respect to homotopic cocycles, have isomorphic <i>K</i>-theory.</p>

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Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies

  • 期刊论文

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  • 发表日期：

    2025年6月17日

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  • Alexander Mundey,
  • Aidan Sims

摘要

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted \(C^*\) C ∗ -algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that does not induce a homomorphism even between (untwisted) Toeplitz algebras. We prove that the twisted \(C^*\) C ∗ -algebras of a jointly faithful self-similar action of a countable discrete amenable groupoid on a row-finite k-graph with no sources, with respect to homotopic cocycles, have isomorphic K-theory.